Avoiding undesired human interaction wrenches

for estimation in human-robot manipulation tasks

Denis Cehajic, Pablo Budde gen. Dohmann, and Sandra Hirche

Abstract—Knowing accurately the kinematic and dynamicparameters of a manipulated object is required for commoncoordination strategies in physical human-robot interaction. Pa-rameter bias may disturb the human during interaction andbias the recognition of the human motion intention. This workpresents a strategy allowing the tracking of human motion andinducing the motions necessary for identification. Such motionsare projected in the null space of the partial grasp matrix,relating the human and the robot redundant motion directions,to avoid the disturbance of the human motion. The approach isevaluated in a human-robot object manipulation setting.

I. INTRODUCTION

Physical human-robot collaboration (pHRI) is envision in

multiple application domains in the future, such as industrial,

domestic- and service-related. As the human and the robot are

directly coupled, the behavior of the robot directly influences

that of the human and vice versa. The interaction of the robot

during cooperation with the human is achieved through the

impedance/admittance control in combination with the object

dynamics model [1]–[3]. Wrenches applied on the object are

usually transformed to the robot frame using the relative

kinematics. Desired wrenches needed to achieve a desired

motion are calculated through the inverse dynamics model [1],

[2]. Any bias in either the relative kinematics, i.e. relative

displacement and orientation of the frames, and/or the object

dynamic parameters, i.e. mass, center of mass, and moments

of inertia, results in incorrectly calculated robot wrenches,

which may disturb the human partner during interaction or

when performing a desired motion [4], [5].

Since in many real-life physical human-robot interaction

applications the relative kinematics and object dynamics are

unknown, an online estimation strategy is indispensable. A

few unique challenges arise in parameter estimation in pHRI:

(i) the human is usually unaware of the required motion for

identification, (ii) the robot solely executing the identification-

relevant motion may cause undesired human wrenches and

may disturb the human partner [4], (iii) the desired estima-

tion strategy needs to account for the human presence by

simultaneously allowing the human partner to perform a de-

sired motion while inducing an identification-relevant motion,

necessary for parameter convergence. This work presents an

approach achieving the estimation of the unknown parameters,

while avoiding undesired human interaction wrenches, thus

enabling the human to perform a motion.

The research leading to these results has received funding from theEuropean Union Seventh Framework Programme FP7/2007-2013 under grantagreement n◦ 601165 of the project ”WEARHAP - WEARable HAPtics forhumans and robots”.

D. Cehajic, P. Budde gen. Dohmann, and S. Hirche are with the Chair ofInformation-oriented Control, Technical University of Munich, Germany.{denis.cehajic, pablo.dohmann, hirche}@tum.de

II. MODELING THE HUMAN-ROBOT MANIPULATION TASKS

We consider a task where a human and a robot co-

operatively manipulate a rigid object in SE(3) with un-

known relative kinematics and object dynamics as depicted

in Fig. 1. Coordinate frames of the human, robot, and

object are denoted with {h}, {r}, and {o}, respectively.

The object frame coincides with the object’s center of

mass. All coordinate frames are fixed. The pose is rep-

resented by xi = [pTi , q

Ti ]

T ∈ SE(3) ∀i ∈ h, r, o containing

the translation pi ∈ R3, and orientation qi ∈ S3 represented

by a unit quaternion. Let xi = [vTi ,ω

Ti ]

T ∈ se(3) be a

twist vector containing the translational vi ∈ R3, and

angular velocity ωi ∈ R3, and let xi = [vT

i , ωTi ]

T contain

translational and angular accelerations. Each agent applies

wrench ui = [fTi , tTi ]

T ∈ R6 with fi ∈ R

3 as the force

and ti ∈ R3 as the torque applied at the grasping point.

Inconsistent robot motion, i.e. robot motion not matching

the human motion, causes undesired interaction wrenches,

which disturb the human during interaction. A common human

dynamics model suggests that the human applies a wrench uh

when there is a difference between the desired and the actual

human motion, expressed, as an example, as

Kh(xdh − xh) = uh (1)

with xdh and xh as the desired and actual human motion,

and Kh ∈ R6×6 as the translational and rotational stiffness of

the human wrist. From (1) it can be inferred that zero human

wrench, i.e. uh = 0, indicates a zero difference between the

desired and actual human pose, i.e. xdh = xh.

In order to estimate the unknown parameters (any of the

parameters in Fig. 1), the object motions need to be sufficiently

exciting [6]. Performing such motion may cause undesired

human interaction wrenches (1) and may disturb the human

when performing a desired motion. We aim at performing

{h}

{r}{o}

rph,rqh

rpo

mo,Jo

Fig. 1: Cooperative human-robot object manipulation task:

Relative kinematics is parametrized with the displacementrph, and orientation rqh (orange); Object dynamics with the

mass mo, center of mass rpo, and inertia matrix Jo (blue).

identification-relevant motions, such that the difference to the

human desired motion is minimal, according to (1), as

minxr

||uh||2 . (2)

III. AVOIDING UNDESIRED HUMAN WRENCHES

We derive an appropriate robot motion inducing

identification-relevant motions and avoiding undesired

human interaction wrenches. During interaction the human

and the robot do not necessarily apply wrenches along

all directions. Let ui ∈ Rni denote applied wrenches of

a partner, with ni as the partner’s input dimensionality.

Let hGr ∈ Rnh×nr denote the partial grasp matrix relating

human and robot applied wrenches. In the following, we

present a strategy for the case nh < nr, i.e. when the robot

has greater input dimensionality than the human.

The internal wrench component results in no motion and it

lies in the null space of hGr [7]

null(hGr) = {ur|hGrur = 0} . (3)

from which it can be inferred that minimal disturbance of (1)

is achieved if the identification-relevant motions lie in the null

space of hGr. This means that the non-redundant directions

can be chosen for inducing an identification-relevant motion

achieving (2).

Let xdr denote the robot motion necessary for tracking

a human desired motion and inducing an identification-

relevant motion satisfying the persistent excitation condi-

tion [6], and ¯xid ∈ Rnr−nh as the motions in the directions

not spanned by the human motion along the redundant direc-

tions xRh ∈ R

nh . Motions ¯xid are induced by

xdr =(hGT

r )+xR

h (4)

+ (N(Inr− (hGT

r )+hGT

r ))+(¯xid −N(hGT

r )+xR

h ) ,

where (hGTr )

+xRh is responsible for tracking a desired human

motion along the redundant directions, and the rest of the

expression induces an identification motion ¯xid, in the null

space of hGr, N ∈ R(nr−nh)×nr contains non-redundant

rows of the partial grasp matrix.

IV. EVALUATION

Description: We conducted a small user study to evaluate

the effect of the induced identification motions during a human

motion. The setting consists of a human partner grasping

a handle, a 7 DoF robotic manipulator and a rigid object

(as in Fig. 1). Wrenches of both the human and the robot

are measured by the 6 DoF JR3 force/torque sensors. We

analyze the performance with 5 human participants, who are

instructed to move 0.5 m along the negative y-direction. The

human velocity is estimated using the Kalman filter from

the human position, acquired by the motion tracking system.

We evaluate: (i) the proposed approach (4), (ii) a naive

approach by simply adding the equivalent robot and identi-

fication motions, i.e. xr,naive = xr + xid, and (iii) when no

motion is introduced (xid = 06×1), i.e. following the desired

human motion, such to compare the effects of (i) and (ii).

Each condition is repeated 20 times, totaling in 60 trials per

0

2

4

6

8

10

e

Naive approach

σ

µ

0 0.5 10

2

4

6

8

10

e

0 0.5 1

Time (normalized)

Proposed approach

0 0.5 1

σ

µ

Fig. 2: Interaction error averaged over all trials and subjects:

(left to right) mean µ and variance σ along components

fh,x, fh,y, fh,z, for the naive (top) and proposed (bottom).

subject; the order of all trials is randomized. The induced mo-

tion is xid = [03×1, (ωid)T ]T , where ωid = Ad

2 −Adstep(F d)(rad/s), with the amplitude Ad = [0.2, 0.15, 0.1]T and the

frequency F d = [0.33, 0.71, 0.5]T .

Results: To isolate the effect of undesired interaction we

define the interaction error as e(t) = |fi(t)−µref|σref

, ∀i = 1, 2,

where fi are the human interaction forces of the proposed

and naive interaction, respectively, and µref, σref are the mean

and standard deviation of the reference force fref over all

trials for a single subject. The error is weighted with the

confidence in the desired force, represented by σref. The

resulting interaction error e is then averaged over all trials

for each subject. The averaged interaction errors are depicted

in Fig. 2. It is evident that the proposed approach reduces

the interaction error exerted to the human partner: the mean

is [1.3, 1.0, 1.0]T and the maximum error is [2.4, 1.5, 1.2]T

using the proposed approach, compared to [2.3, 3.8, 1.4]T as

the mean and [3.6, 6.0, 2.1]T as the maximum error using

the naive approach. The proposed approach shows a drastic

improvement in terms of interaction error.

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